Properties

Label 59150.bp
Number of curves $4$
Conductor $59150$
CM no
Rank $0$
Graph

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Show commands for: SageMath
sage: E = EllipticCurve("59150.bp1")
 
sage: E.isogeny_class()
 

Elliptic curves in class 59150.bp

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients Torsion structure Modular degree Optimality
59150.bp1 59150bd4 [1, -1, 1, -1130980, -462640603] [2] 737280  
59150.bp2 59150bd3 [1, -1, 1, -370480, 81201397] [2] 737280  
59150.bp3 59150bd2 [1, -1, 1, -74730, -6340603] [2, 2] 368640  
59150.bp4 59150bd1 [1, -1, 1, 9770, -594603] [2] 184320 \(\Gamma_0(N)\)-optimal

Rank

sage: E.rank()
 

The elliptic curves in class 59150.bp have rank \(0\).

Modular form 59150.2.a.bp

sage: E.q_eigenform(10)
 
\( q + q^{2} + q^{4} - q^{7} + q^{8} - 3q^{9} - 4q^{11} - q^{14} + q^{16} - 2q^{17} - 3q^{18} + O(q^{20}) \)

Isogeny matrix

sage: E.isogeny_class().matrix()
 

The \(i,j\) entry is the smallest degree of a cyclic isogeny between the \(i\)-th and \(j\)-th curve in the isogeny class, in the LMFDB numbering.

\(\left(\begin{array}{rrrr} 1 & 4 & 2 & 4 \\ 4 & 1 & 2 & 4 \\ 2 & 2 & 1 & 2 \\ 4 & 4 & 2 & 1 \end{array}\right)\)

Isogeny graph

sage: E.isogeny_graph().plot(edge_labels=True)
 

The vertices are labelled with LMFDB labels.